Finite Group Databasebeta

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C₂×#5812 #87244

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

1488 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 25 points:

(1,2)(3,4,5)(10,13)(11,16)(12,19)(14,21)(15,22)(17,23)(18,24)(20,25);(10,12,14,20)(11,15,17,18)(13,19,21,25)(16,22,23,24);(10,11,14,17)(12,18,20,15)(13,16,21,23)(19,24,25,22);(4,5)(6,7,8,9)(13,21)(16,23)(19,25)(22,24);(1,2)

Conjugacy classes & character table

108 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 19820);